Combining the Strong Hasse Principle [1]} and
Witt's Cancellation Theorem (see Theorem REF ), we know that an
integral quadratic form is \(k\) -isotropic over \({\mathbb {Q}}\)  if and only if it
is \(k\) -isotropic over \({\mathbb {Q}}_p\)  for all primes \(p\)  and over \(\mathbb {R}\) .
Applying a theorem of Poonen and Stoll [2]} we deduce the
following result.
